SOLUTION: I'm not sure if this ones the right category... Anyway, for this problem I need to simplify all square roots and answers should not be decimals. Factor or solve the following: 3x

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I'm not sure if this ones the right category... Anyway, for this problem I need to simplify all square roots and answers should not be decimals. Factor or solve the following: 3x      Log On


   

Question 1174688: I'm not sure if this ones the right category...
Anyway, for this problem I need to simplify all square roots and answers should not be decimals. Factor or solve the following:
3x⁴+2x²+3=2x⁴-2x²+8
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E4%2B2x%5E2%2B3=2x%5E4-2x%5E2%2B8
3x%5E4%2B2x%5E2%2B3-2x%5E4%2B2x%5E2-8=0
x%5E4%2B4x%5E2-5=0
x%5E4-x%5E2%2B5x%5E2-5=0
%28x%5E4-x%5E2%29%2B%285x%5E2-5%29=0
x%5E2%28x%5E2-1%29%2B5%28x%5E2-1%29=0
%28x%5E2%2B5%29%28x%5E2-1%29=0
%28x%5E2%2B5%29%28x-1%29%28x%2B1%29=0
solutions:
if %28x%5E2%2B5%29=0+=> x%5E2=-5 => x=sqrt%28-5%29 => x=i%2Asqrt%285%29 or x=+-i%2Asqrt%285%29
if %28x-1%29+=0=>+x=1
if %28x%2B1%29=0=> x=-1
so, real roots are:
x=1
x=-1
and complex roots are:
x=i%2Asqrt%285%29
x=+-i%2Asqrt%285%29

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

Surely, it goes to wrong category.


May I ask you to omit this your mantra about a "category" : it really irritates when you repeat it every time . . .


Thank you.